(375c) Properties of Dilute Suspensions of Ellipsoidal Particles, or How I Learned to Love Shapes Other Than Spheres

What are the rheological properties of a dilute suspension of (not necessarily axisymmetric) ellipsoidal particles? While Jeffery first worked out the fluid mechanics of ellipsoidal particles in Stokes flow over a century ago and certain works have studied the statistical distributions of ellipsoidal particles in Stokes flow (e.g., those by Leal, Hinch, Scheraga, Kuhn, Kuhn, and Saito among others), questions about the rheological behavior of general ellipsoidal particles still remain unanswered, in large part due to computational challenges and the fact that non-axisymmetric ellipsoidal particles exhibit quasi-periodic motion. In this work, a manifold-constrained finite volume algorithm is developed to evaluate efficiently the ensemble-averaged stresslet contributions of ellipsoidal particles interacting with a background flow field and subject to thermal fluctuations. Non-Newtonian rheological properties are quantified, and the shapes of maximally viscosifying ellipsoids under geometrical constraints will be discussed (with some unexpected results).